How, under Labour, a working-class baby now has 'far less chance' of getting ahead in society

Mr Milburn, a close friend of Tony Blair, said that "shamefully", Britain has become a less socially mobile society in recent years, questioning whether today's deprived children will be able to break out of poverty in adulthood.

Labour has made narrowing the gap between economic groups a key objective of social policy and Mr Milburn's comments handed more ammunition to the government's critics.

"Most are better off and prosperity has risen. But we have to be honest about this: inequality has remained stubbornly wide in our country," Mr Milburn said. "Over many decades, social mobility has slowed down when it ought to be speeding up."

Mr Milburn, who left the Cabinet in 2005 but remains close to the Prime Minister, warned of the creation of an "80-20 society," where 80 per cent prosper but 20 per cent get left behind.

Speaking on BBC Radio Four, he asked: "Is it possible that we can imagine a kid growing up today, growing up like I was, in a staunchly working-class community, living on a council estate, living in one of the more deprived areas, is it possible that in 25 years' time we can imagine them in the Cabinet?"

He concluded: "The honest and possibly shameful answer is that we can't. I think that is a huge matter of regret, and it should impel all politicians to do everything they can to provide more opportunities for those at the bottom end."

Mr Milburn's view is at odds with that of Chancellor Gordon Brown, who said in April 2005: "This is not just a Britain of social mobility for some; it is a Britain where opportunity is open to all."

Social mobility, a child's chance of ending up in a higher economic class than its parents, is notoriously hard to measure, but some studies may support Mr Milburn's analysis of earlier decades.

A London School of Economics report in 2005 showed declining social mobility in Britain, with more poor children becoming poor adults, and more rich children staying rich in later life. The LSE team found that 31 per cent of boys born in 1958 in the lowest-earning group stayed there in adulthood. But that rose to 38 per cent of boys born in 1970.

Internationally, many researchers say that Britain's social mobility is much lower than other western democracies, and comparable only with that in the United States.

According to the LSE data, 27 per cent of British boys born in 1970 ended up in the same earnings group as their parents. By contrast, 14 per cent of Canadian boys born between 1967 and 1970 ended up in the same earnings group as their parents.

Under David Cameron, the Conservatives have attacked the government over social mobility, and Philip Hammond, the party's welfare spokesman, said: "Labour's narrowly focused attempts to tackle poverty through the welfare system rather than addressing the root causes of deprivation have actually reduced social mobility and suppressed aspiration."

Danny Alexander, the Lib Dem social exclusion secretary, also blamed the government for creating a "state of benefit dependency that means that for too many families, unemployment and benefits claiming have become inherited conditions".

But Jim Murphy, the Glasgow MP and minister overseeing social mobility, last night told The Scotsman the reality is more complex than the critics had suggested. Because social mobility can only be accurately measured over a generation, he said, society today is really a reflection of government policy 20 or so years ago.

"This is a lazy analysis that mistakes the nature and timescale of social mobility," Mr Murphy said.

"The time of optimum influence on the social mobility of today's 30-something generation was in their childhood, so today's reality is a reflection of policy in the mid-1980s."